The value of x that makes sense in this context is; 32.
The dimensions of the new garden is; 64 by 16.
<h3>How to find the real dimensions of the rectangle?</h3>
The expression that represents the problem statement is;
x² = (2x)(x – 16)
Expanding the bracket gives us;
x² = 2x² – 32x
x² - 32x = 0
x(x - 32) = 0
Thus; x = 0 or x = 32
x can't be 0 and as such the value of x is 32.
Thus;
The length of the new garden is; l = 2x = 64.
The width of the new garden is; w = x - 16 = 32 - 16 = 16
The dimensions of the new garden are therefore; 64 by 16
Read more about Rectangle Dimensions at; brainly.com/question/17297081
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What we know:
line P endpoints (4,1) and (2,-5) (made up a line name for the this line)
perpendicular lines' slope are opposite in sign and reciprocals of each other
slope=m=(y2-y1)/(x2-x1)
slope intercept for is y=mx+b
What we need to find:
line Q (made this name up for this line) , a perpendicular bisector of the line p with given endpoints of (4,1) and (2,-5)
find slope of line P using (4,1) and (2,-5)
m=(-5-1)/(2-4)=-6/-2=3
Line P has a slope of 3 that means Line Q has a slope of -1/3.
Now, since we are looking for a perpendicular bisector, I need to find the midpoint of line P to use to create line Q. I will use the midpoint formula using line P's endpoints (4,1) and (2,-5).
midpoint formula: [(x1+x2)/2, (y1+y2)/2)]
midpoint=[(4+2)/2, (1+-5)/2]
=[6/2, -4/2]
=(3, -2)
y=mx=b when m=-1/3 slope of line Q and using point (3,-2) the midpoint of line P where line Q will be a perpendicular bisector
(-2)=-1/3(3)+b substitution
-2=-1+b simplified
-2+1=-1+1+b additive inverse
-1=b
Finally, we will use m=-1/3 slope of line Q and y-intercept=b=-1 of line Q
y=-1/3x-1
Answer:
point form: (5/2, 0)
equation form: 5/2, y=0
Step-by-step explanation:
The process to simplify a [proper] fraction is always the same:
-- If the numerator and denominator have a common factor,
then divide them both by it.
-- If they still have a common factor, then divide them both by that one.
-- Keep doing that until their only common factor is ' 1 '.
That's when the fraction is in simplest form.
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A slightly different approach is:
-- Find the <em><u>greatest</u></em> common factor of the numerator and denominator.
-- Divide the numerator and denominator both by it.
-- The fraction is then in simplest form.
==========================================
As an example, let us do some work on the fraction you have provided:
<em> 25 / 100</em> .
-- The factors of 25 are 1 , 5 , and 25 .
-- The factors of 100 are 1 , 2 , 4 , 5 , 10 , 20 , 25 , 50 , and 100 .
-- The factors that are common to 25 and 100 are 1 , 5 , and 25 .
-- The greatest one of those is 25 .
So ' 25 ' is the number by which you should divide the numerator and denominator of your fraction. When you do that, the fraction will be in its simplest form.
